Autonomous and policy-induced behavior change during the COVID-19 pandemic: Towards understanding and modeling the interplay of behavioral adaptation

Changes in human behaviors, such as reductions of physical contacts and the adoption of preventive measures, impact the transmission of infectious diseases considerably. Behavioral adaptations may be the result of individuals aiming to protect themselves or mere responses to public containment measures, or a combination of both. What drives autonomous and policy-induced adaptation, how they are related and change over time is insufficiently understood. Here, we develop a framework for more precise analysis of behavioral adaptation, focusing on confluence, interactions and time variance of autonomous and policy-induced adaptation. We carry out an empirical analysis of Germany during the fall of 2020 and beyond. Subsequently, we discuss how behavioral adaptation processes can be better represented in behavioral-epidemiological models. We find that our framework is useful to understand the interplay of autonomous and policy-induced adaptation as a “moving target”. Our empirical analysis suggests that mobility patterns in Germany changed significantly due to both autonomous and policy-induced adaption, with potentially weaker effects over time due to decreasing risk signals, diminishing risk perceptions and an erosion of trust in the government. We find that while a number of simulation and prediction models have made great efforts to represent behavioral adaptation, the interplay of autonomous and policy-induced adaption needs to be better understood to construct convincing counterfactual scenarios for policy analysis. The insights presented here are of interest to modelers and policy makers aiming to understand and account for behaviors during a pandemic response more accurately.

In the following, we present the models that support the results presented in Section 4.1.We specify our most parsimonious model as Model A ln# !,# % =  $ +  % ln# !,# + 1% +  &  !,# +  !+  !,# where  !,# represents the dependent variable, the percentage change in mobility in federal state j on day t, relative to the average of the same month in the year 2019 [1].Furthermore,  !,# represents the 7-day-incidence and  !,# the stringency of containment measures in state j at day t [2,3].We calculate the natural log of incidence due to the at times exponential growth of case numbers and add one to address zeros in the data. !represents the individual fixed effect at the state level,  !,# the error term.Note that we also dropped either predictor and tested whether including national incidence levels had a significant effect, as was the case in [4].Neither resulted in an improved model fit.
As the raw data indicated significant changes in mobility patterns between weekdays, Saturdays and Sundays, we added individual indicator variables ( # &  # ) to account for this heterogeneity: The weather changes in the fall likely impact mobility patterns.We include the daily average temperature temp and the daily average precipitation precip in state j at day t.This data was obtained from Deutscher Wetterdienst [5], Germany's national meteorological service.The data for all 83 weather stations were downloaded and spatially interpolated for each federal state using the inverse distance weighting method.
Finally, we estimate a model in which we drop the stringency index ( !,# ) as a predictor variable and instead introduced a categorical variable phase which refers to the extent to which nationallevel NPIs were implemented and depends on the date of each observation.Any date before November 2 receives the value "local measures", from November 2 to December 15 the value "lockdown light" and thereafter "lockdown hard".This may also mitigate potential multicollinearity issues between  !,# and  !,# , which can occur if increased stringency follows increased incidence levels, as it was the case in some federal states.The model is thus specified as: Note that daily the inclusion of weather data did not lead to improvements in model fit in the specification of Model D, perhaps because the different NPI phases roughly coincide with decreasing temperature levels and increased precipitation in fall.The variables temp and precip were thus not included in Model D. Detailed regression results can be found in S1 Table 1.The results indicate that the sign of stringency and incidence are as expected and robust across all models, with slight reductions in effect sizes due to the incorporation of additional predictors.With declining temperature and higher precipitation mobility is reduced as should be expected.In Models A and B, this seasonal trend seemed to be attributed to increases in stringency and incidence over the same period.Interestingly, the introduction of the variable phase as an ordinal measure of stringency improved model fit while reducing the effect of incidence slightly, indicating that more variance in the data can be explained when measuring ordinal stringency at the national level.In .We therefore report our regression results with standard errors robust to heteroscedasticity and autocorrelation, using the method of [7].Models were estimated and standard errors calculated using the R package fixest [8].As the models are implemented using a within transformation, multicollinearity that might have existed between time-related predictors and individual fixed effects is largely mitigated.Robust standard errors (RSE) and confidence intervals (CI) were calculated using the Newey West method as described by [8].

S1
The table with model outputs was generated using the R package sjPlot [9]

S1Fig 1 .
Fig 4 in Section 4.1, a marginal effects plot for Model D is presented.Below, in S1 Fig 1, marginal effects for both state-level stringency and incidence in Model C are presented, depicting two values of the other predictor, and assuming a weekday mean values for temperature and precipitation.Marginal effects of policy stringency and 7-day incidence in Model C. The plot was generated using the R package ggeffects [6].The models were subjected to diagnostic tests common for this model class: The Pesaran CD (Cross-Sectional Dependence) test indicated presence of heteroscedasticity and a Durbin-Watson test suggested presence of some serial correlation (see also the diagnostics plots in panels C and D of S1 Fig 2)